Electronic Raman scattering from La 0.7Sr 0.3MnO 3 exhibiting giant magnetoresistance
Rajeev Gupta and A. K. Sood*
Department of Physics, Indian Institute of Science, Bangalore, India 560 012
R. Mahesh and C. N. R. Rao
Solid State and Structural Chemistry Unit, Indian Institute of Science, Bangalore, India 560 012
Raman scattering experiments on metallic La 0.7Sr 0.3MnO 3 have been carried out using different excitation
wavelengths as a function of temperature from 15 K to 300 K. Our data suggest a Raman mode attributed to
electronic excitations centered at 2100 cm 21 whose intensity decreases with increasing temperature. If the
Raman mode is attributed to single-particle excitation associated with the fluctuations of the mass tensor, the
decreased intensity would then imply a reduction in the density of states at the Fermi energy with increasing
temperature
Recent observations of colossal magnetoresistance have
stimulated a renewed interest in the electronic properties of
doped La 12x A x MnO 32 d (A5Sr, Ba, Ca, Pb, and vacancies!
and other transition metal oxides having strong electron
correlations.1 The rich phase diagram of La 12x Sr x MnO 3
shows a variety of phases like paramagnetic insulator, ferromagnetic metal, paramagnetic metal, spin-canted insulator,
and ferromagnetic insulator as a function of doping x and
temperature. For 0 ,x, 0.2, the materials are insulating at
all temperatures and are antiferromagnetic or ferrimagnetic
at low temperatures. In the range 0.2 ,x, 0.5 the system
shows a temperature induced transition at T c (x) from the
ferromagnetic metal at T,T c to a paramagnetic insulator.
The end member (x 5 0! is a charge transfer antiferromagnetic insulator having gap corresponding to the charge transfer excitation from oxygen 2p to a manganese 3d state. Out
of the ~42x) manganese d electrons, three electrons occupy
the tightly bound d xy , d yz , and d xz orbitals with very little
hybridization with the oxygen 2p states and can be considered as a local spin S c of 3/2. The remaining ~12x! electrons
occupy the e g state made of the d x 2 2y 2 and d z 2 orbitals and
are strongly hybridized. There is a strong exchange interaction J H ~Hund’s coupling! between the 3d t 2g local spin and
the 3d e g conduction electron. The e g level is further split
2↑
into e 1↑
g and e g due to the Jahn-Teller ~JT! effect. The
↑
2↑
1↑ 1↓
t 2g -e g and e g -e g separation is about 2 eV as calculated by
Satpathy et al. using the local spin density approximation.2
2↑
The estimate of the JT split e g band, namely, e 1↑
g – eg 5
4E 0 , is 2.4 eV. It can, however, range from 0.4 eV to 4 eV as
argued by Millis.3
The metal-insulator transition in the intermediate doping
range is qualitatively understood using the Zener’s ‘‘doubleexchange’’ ~DEX! model, in which the e g electron hopping
from site i to j must go with its spin parallel to S ic to its spin
parallel to S cj . Millis et al.4 have shown that DEX alone
cannot explain many aspects like the low transition temperature T c and the large resistivity of T.T c phase or the sudden
drop in resistivity below T c . They have proposed that, in
addition to DEX, there is a strong electron phonon coupling
such that the slowly fluctuating local Jahn-Teller distortions
localize the conduction band electrons as polarons. As the
temperature is lowered, the effective hopping matrix element
t eff characterizing the electron itineracy increases and the ratio of JT self-trapping energy E JT to t eff decreases. The JT
distortion has to be dynamic because a static JT effect would
cause a substantial distortion of the structure and the material
would be antiferromagnetic. Coey et al.5 have argued from
the experimental magnetoresistance data that for T,T c , the
e g electrons are delocalized on an atomic scale but the spatial
fluctuations in the Coulomb and spin-dependent potentials
tend to localize the e g electrons in wave packets larger than
the Mn-Mn distance. It has also been noted5,6 that doped
manganites are unusual metals, having resistivities greater
than the maximum Mott resistivity ~1–10 mV cm! and a
very low density of states at the Fermi level.7
Optical
conductivity
measurements
on
La 0.825Sr 0.175MnO 3 as a function of temperature by Okimoto
et al.8 in the range 0–10 eV show a band at ; 1.5 eV and
spectral weight is transferred from this band to low energies
with decreasing temperature. This band at ; 1.5 eV has been
interpreted due to the interband transitions between the
exchange-split spin-polarized e g bands. At T,T c , the conductivity spectrum is dominated by intraband transitions in
the e g band. A similar feature at ; 1 eV has been observed
in Nd 0.7Sr 0.3MnO 3 which shifts to lower energies with decreasing temperature which is argued to be consistent by
taking into account the dynamic JT effect.9 There is no reported work on Raman scattering in these systems. Millis3
has suggested that the transition between the e g levels split
by the JT interaction can be Raman active. The electronic
Raman scattering can be observed from the single-particle
and collective plasmon excitations. The crystal structure with
space group R3c (D 63d ) with two formulas in the unit cell
has A 1g and 4E g Raman-active modes. Our objective was to
study vibrational and electronic Raman scattering in doped
manganites as a function of temperature. In this paper
we report electronic Raman scattering from doped
La 12x Sr x MnO 3 (x 5 0.3! from 15 K to 300 K.
Polycrystalline pellets of La 0.7Sr 0.3MnO 3 prepared by
citrate-gel route and sintered at 1473 K with an average grain
size of ; 3.5 m m were used.10 The samples on which detailed studies were done have a resistivity of 0.4 mV cm at
FIG. 1. Raman spectra recorded with different excitation wavelengths 514.5 nm and 488 nm at 15 K. The solid lines show the
fitted function @Im(21/e )# to the data shown by open circles.
FIG. 2. Raman spectra at different temperatures using 488 nm
excitation wavelength. Note that the intensity of the mode decreases
as temperature increases.
15 K and 3.5 mV cm at 300 K. It shows a phase transition
from a ferromagnetic metal to a paramagnetic insulator at
T c ; 380 K. The Raman measurements were carried out in
the spectral range of 200–6000 cm 21 , at different temperatures from 15 K to 300 K. The spectra were recorded in the
back scattering geometry using Spex Ramalog with photon
counting detector ~photomultiplier tube RCA C 31034 with
GaAs cathode! using 514.5 nm and 488 nm lines of an argon
ion laser ~power density of ; 1500 W cm 22 at the sample!.
The spectra have not been corrected for the spectrometer
response. Pellets of thickness ; 2 mm were mounted on the
copper cold finger of the closed-cycle helium refrigerator
~RMC model 22C CRYODYNE! using thermally cycled GE
~M/s. General Electric! varnish. The temperature of the cold
finger was measured using a platinum 100 sensor coupled to
a home made temperature controller. The temperatures
quoted are those of the cold finger and were measured to
within a accuracy of ; 2 K. The experiments were done on
three differently prepared pellets of La 0.7Sr 0.3MnO 3 and the
results were similar to the ones reported here.
Figure 1 shows the recorded spectra at 15 K for the two
different excitation wavelengths l L of 514.5 and 488 nm.
Figure 2 shows the spectra recorded at different temperatures
using the excitation wavelength of 488 nm. The spectrum
was featureless at room temperature and hence is not shown.
A small hump at ; 1000 cm 21 in the spectrum recorded
using 514.5 nm radiation is perhaps due to the spectrometer
response. We have not been able to observe Raman scattering from the phonons. This may be due to the fact that the
deviations from the cubic structure are rather small ~optic
phonon modes in perovskite structure with cubic symmetry
of O 1h are not Raman active!.
Inelastic light scattering can occur from single-particle or
collective excitations ~plasmons! of free carriers in metals
and heavily doped ~degenerate! semiconductors. The singleparticle excitations corresponding to the charge density fluctuations in metals and semiconductors with a single sheeted
Fermi surface are screened at low frequencies in a selfconsistent manner by the carriers themselves.11,12 Thus, in
simple free-electron-like carrier systems, light scattering
from these single-particle excitations is not observed and
only a peak at the plasma frequency can be seen. However,
in a system with anisotropic Fermi surface like in a multivalley semiconductor, charge density fluctuations in various
equivalent valleys can be out of phase and exactly cancel
others. These excitations do not carry any net charge and
hence are not screened by the carriers. These excitations produce fluctuations of the mass tensor resulting in lowfrequency Lorentzian-like line shape. The theory proposed
by Ipatova et al.13 based on the collision-dominated electronic transport due to strong scattering of carriers by the
impurities can explain the observed Raman scattering due to
mass tensor fluctuations in n-type Si,14 n-type Ge,15 and
high-temperature superconductors.16 In this theory the Raman scattering cross section is given by
I ~ v ! 5 @ n ~ v ,T ! 11 #
where G is the scattering rate and
B5
e4
N~ «F!
pc4
KU S
ê L
BvG
~ v 2 1G 2 !
~1!
,
K LD U L
] 2« ka
] 2« ka
2
] k] k
] k] k
2
ê S
.
~2!
Here « k a is the energy of the electron in band a with the
momentum \kW and N(« F ) the density of states at the
Fermi level per unit volume. ê L (ê S ) is the polarization of
the incident ~scattered! radiation. The brackets ^& denote
the Fermi surface average, ^ f k & [ ( k a f k d (« F 2« k a )/
( k a d (« F 2« k a ). Equation ~2! can also be rewritten in terms
of the effective mass tensor,
B5
e4
Q 21 2 ^ m
Q 21 & ! ê S u 2 & .
N ~ « F ! ^ u ê L ~ m
pc4
~3!
The term @ n( v ,T)11 # in Eq. ~1! is the usual Bose-Einstein
population factor. In Fermi liquid theory, G is frequency dependent and is taken to be G( v ) 5 G 0 1 a v 2 . The parameter a depends on the electron correlation effects and relates
to the enhancement of the effective mass of the carriers.
Equation ~1! exhibits a maximum at v ;G 0 and the peak
FIG. 3. Theoretical curves generated using Eq. ~1! for different
values of the scattering strength B.
intensity is proportional to B. Figure 3 shows a plot of Eq.
~1! for different values of the strength parameter B, G 0 5
2100 cm 21 , and a 5131023 cm 21 . The value of a is close
to the value used17 to explain electronic Raman scattering in
filling-controlled metals Sr 12x La x TiO 3 . It can be seen that
the plots in Fig. 3 are very similar to our observed Raman
line shapes in Figs. 1 and 2. We have not fitted the data
quantitatively to Eq. ~1! because the signal-to-noise ratio of
the data is not so high and the data is not corrected for the
spectrometer response over the entire spectral range. The observed decrease of Raman peak intensity with increasing
temperature implies that B and hence N(« F ) decrease as the
temperature is raised. The decrease of density of states at the
Fermi energy with increasing T has been seen in photoemission studies7 and is argued to be related to the change in
electron correlation strength U/W, where U is the effective
Coulomb interaction strength and W is the d-band width. As
T increases, U/W increases due to the combined effect of
decreasing W as well as effective increase of U resulting
from the decreasing degree of ferromagnetic order. The increase in U/W results in a transfer of single-particle spectral
weight from the coherent features near « F to the incoherent
part at higher energies.7
Another likely candidate for the observed Raman mode
can be a collective electronic excitation, namely, the plasmon. At this stage without the data on the polarization selection rules on single-crystal samples, it is not possible to decide if the observed mode is associated with the singleparticle excitation mentioned above or the plasmon. Raman
scattering from the plasmon can be expressed by11,12
I ~ v ! 5 @ n ~ v ,T ! 11 # Im@ 21/e ~ v !# ,
~4!
*Author to whom correspondence should be addressed. Electronic
address: asood@physics.iisc.ernet.in
1
S. Jin, T.H. Tiefel, M. McCormack, R.A. Fastnacht, R. Ramesh,
and L.H. Chen, Science 264, 413 ~1994!.
2
S. Satpathy, Z.S. Popovic, and F.R. Vukajlovic, Phys. Rev. Lett.
76, 960 ~1996!.
3
A.J. Millis ~unpublished!.
where the dielectric function e ( v ) can be ~in the simplest
Drude form! e ( v ) 5 e ` @ 12 v 2p /( v 2 1i v G p ) # , e ` is the
high-frequency dielectric constant, v p is the plasma frequency, and G p is the relaxation rate. The solid curves in Fig.
1 correspond to the best fit by Eq. ~4! with parameters v p 5
2100 cm 21 and relaxation rate G p 5 2600 cm 21 ~for spectra
recorded using 514.5 nm radiation!, and v p 5 2300 cm 21 ,
G p 5 2600 cm 21 ~for spectra recorded using 488 nm!. Using
v 2p 5 4p n p e 2 /( e ` m ! m e ) where n p is the number density of
carriers of effective mass m ! m e (m e is the mass of an electron!, e ` 5 4.9 ~same18 as that of LaMnO 3 ), n p /m ! ; 2.43
10 20 cm 23 . The number density calculated from the doping
of 0.3 carriers per unit cell of cell volume6 64 Å 3 is n d 55
310 21 cm 23 . Taking the effective mass of the carriers to be
m ! 5 1, it is seen that n p 5 0.05n d , i.e., the actual number
of carriers is less than (12x) per manganese site. This can
be related to the model of Coey et al.5 wherein the e g electrons though delocalized on atomic scale are in magnetically
localized wave packets spread over the Mn-Mn separation. If
the localization energy of some carriers is less than \ v p ,
they will not participate in the collective plasmon excitation.
The localization of the carriers need not be as magnetic polarons but may involve lattice polarons as envisaged by
Millis.3,4 The reduced number of carriers is consistent with
the Hall measurements of Hundley as referred by Roder
et al.19 The observed low density of states at Fermi energy7
also corroborates the less number of carriers deduced from
v p . Perhaps m ! can be greater than 1 which will reduce the
difference between the n p and n d . The dc resistivity in the
free electron model is r 5 m/n p e 2 t , where t is the relaxation time of the carriers. Putting t 21 5 G p , r can be expressed in terms of v 2p and G p as r 5 4 p G p /( e ` v 2p ). Taking G52600 cm 21 and v p 5 2100 cm 21 , we get r 5 7.2
mV cm, which is remarkably close to the measured values.
The r (T) and hence G increases with temperature and can
therefore result in substantial reduction of Raman intensities,
as seen in our experiments. The observed Raman frequency
is much smaller than the estimated 4E 0 and hence is not
likely to be associated with the transition between the JTsplit e g bands.
In conclusion, we have observed Raman scattering from
electronic excitations in the low-temperature metallic phase
of La 0.7Sr 0.3MnO 3 . Further polarized Raman experiments on
these materials especially on single crystals can provide
more clues as to the exact nature and symmetry of these
excitations.
We thank Professor T.V. Ramakrishnan, R. Mahendiran,
Professor A.K. Raychaudhuri, and Professor B.S. Shastry for
useful discussions. A.K.S. thanks Department of Science and
Technology, India and R.G. thanks CSIR for the financial
assistance.
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